Mixed uncertainty analysis on pumping by peristaltic hearts using Dempster-Shafer theory

Area of Science:

• Computational Fluid Dynamics
• Uncertainty Quantification
• Biomedical Engineering

Background:

• Peristaltic pumping is crucial in biomedical systems like artificial hearts.
• Accurate modeling requires handling both stochastic (random) and epistemic (belief-based) uncertainties.
• Existing methods may not fully capture mixed uncertainty propagation.

Purpose of the Study:

• To introduce a numerical strategy for mixed uncertainty propagation using probability and Dempster-Shafer theories.
• To apply this strategy to a computational model of peristalsis in a heart-pumping system.
• To quantify uncertainty in quantities of interest (QoIs) using belief functions.

Main Methods:

• Representing stochastic uncertainty with random variables and epistemic uncertainty with belief functions.
• Propagating mixed uncertainty through the peristalsis model.
• Utilizing physics-constrained generalized polynomial chaos (gPC) for surrogate modeling to reduce computational cost.
• Performing global sensitivity analysis to identify key uncertain factors.

Main Results:

• Developed a numerical method to propagate mixed uncertainty in peristaltic pumping models.
• Quantified uncertainty in QoIs (flow volume, cost of transport, work) using belief functions.
• Sensitivity analysis identified critical uncertain parameters, with results compared across different peristalsis models.
• gPC surrogates effectively approximated full simulations, reducing computational expense.

Conclusions:

• The proposed numerical strategy effectively handles mixed uncertainty in complex biomedical systems.
• Belief functions provide a robust way to represent and propagate epistemic uncertainty in QoI statistics.
• The method aids in identifying critical design parameters and improving the reliability of computational models for heart-pumping systems.